No that is not what is boils down to, i dont even agree that prison should be viewed as a punishment at all
Prison should be for separating a person that is a danger to others until such time they are no longer a danger to others. Judges often have a bad record at picking who will be a danger and who will not thus by default for public safety the public demands people convicted of crimes be sent away for a long time to maximize the possible safety of the public at the expense of the individuals that get caught up in the system
We know that past a certain point harsher punishments in general are not a deterrent to people committing crimes so we need the public to grow a spine and reject the idea of excessive sentences since while it makes them feel safe, it's just putting them at further risk. Some facts are a hard sell to people though, especially when they're afraid.
We have a huge problem with mass incarceration in the US and the treatment of people we lock up and the conditions of those facilities need major reform, but I don't think we should abandon the idea of locking people up as a punishment entirely.